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A Fast Time-Stepping Strategy for Dynamical Systems Equipped With a Surrogate Model

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dc.contributor.authorRoberts, Stevenen
dc.contributor.authorPopov, Andrey A.en
dc.contributor.authorSarshar, Arashen
dc.contributor.authorSandu, Adrianen
dc.date.accessioned2023-02-28T14:18:23Zen
dc.date.available2023-02-28T14:18:23Zen
dc.date.issued2022-01-01en
dc.date.updated2023-02-25T22:42:04Zen
dc.description.abstractSimulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge–Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. We provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.en
dc.description.versionAccepted versionen
dc.format.extentPages A1405-A1427en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1137/20M1386281en
dc.identifier.eissn1095-7197en
dc.identifier.issn1064-8275en
dc.identifier.issue3en
dc.identifier.orcidSandu, Adrian [0000-0002-5380-0103]en
dc.identifier.urihttp://hdl.handle.net/10919/113997en
dc.identifier.volume44en
dc.language.isoenen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleA Fast Time-Stepping Strategy for Dynamical Systems Equipped With a Surrogate Modelen
dc.title.serialSIAM Journal on Scientific Computingen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherJournal Articleen
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Engineeringen
pubs.organisational-group/Virginia Tech/Engineering/Computer Scienceen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineering/COE T&R Facultyen

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